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arXiv · 2505.24530

A Combinatorial Study of the Fixed Point Index

Jesús A. Álvarez López·Alejandro O. Majadas-Moure·David Mosquera-Lois
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Abstract

We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the need for definability, openness, or f-invariance of subspaces -- thereby allowing broader applicability. We also present a natural combinatorial adaptation of the fixed point index that extends the combinatorial Lefschetz number. This extension yields new topological and homotopical invariance results and facilitates the integration of real-valued functions with respect to fixed points.

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Jesús A. Álvarez López, Alejandro O. Majadas-Moure, David Mosquera-Lois. 2025-05-30. A Combinatorial Study of the Fixed Point Index. https://arxiv.org/abs/2505.24530

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